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### Chapter 15

### Solubility Equilibria

Applying equilibrium

The Common Ion Effect

- When the salt with the anion of a weak acid is added to that acid,
- Lowers the percent dissociation of the acid.
- Ex: NaF and HF mixed together
- F- is the common ion

HF ↔ H+ + F-

Adding F- shifts the equilibrium to the left and therefore fewer H+ ions present

The same principle applies to salts with the cation of a weak base.

The calculations are the same as last chapter.

NH4Cl and NH3 (NH4+ is the common ion)

NH3 + H+ NH4+

Buffered solutions

- A solution that resists a change in pH.
- Consists of either a weak acid and its salt or a weak base and its salt.
- We can make a buffer of any pH by varying the concentrations of these solutions.
- Same calculations as before.
- Calculate the pH of a solution that is .50 M HAc and .25 M NaAc (Ka = 1.8 x 10-5)

Na+ is a spectator and the reaction we are worried about is

HAc H+ + Ac-

- Choose x to be small

Initial 0.50 M 0 0.25 M

-x

x

x

Change

Final

0.50-x

x

0.25+x

- We can fill in the table

Initial 0.50 M 0 0.25 M

- Do the math
- Ka = 1.8 x 10-5

Change

-x

x

x

Final

0.50-x

x

0.25+x

x (0.25)

x (0.25+x)

=

1.8 x 10-5 =

(0.50)

(0.50-x)

- Assume x is small

x = 3.6 x 10-5

- Assumption is valid
- pH = -log (3.6 x 10-5) = 4.44

Adding a strong acid or base

- Do the stoichiometry first.
- Use moles not molar
- A strong base will grab protons from the weak acid reducing [HA]0
- A strong acid will add its proton to the anion of the salt reducing [A-]0
- Then do the equilibrium problem.
- What is the pH of 1.0 L of the previous solution when 0.010 mol of solid NaOH is added?

0.25 mol

0.50 mol

- In the initial mixture M x L = mol
- 0.50 M HAc x 1.0 L = 0.50 mol HAc

0.26 mol

0.49 mol

- 0.25 M Ac- x 1.0 L = 0.25 mol Ac-

- Adding 0.010 mol OH- will reduce the HAc and increase the Ac- by 0.010 mole
- Because it is in 1.0 L, we can convert it to molarity

0.25 mol

0.50 mol

0.26 M

0.49 M

- In the initial mixture M x L = mol
- 0.50 M HAc x 1.0 L = 0.50 mol HAc
- 0.25 M Ac- x 1.0 L = 0.25 mol Ac-
- Adding 0.010 mol OH- will reduce the HAc and increase the Ac- by 0.010 mole
- Because it is in 1.0 L, we can convert it to molarity

0.25 mol

0.50 mol

0.26 M

0.49 M

- Fill in the table

HAc H+ + Ac-

Initial 0.49 M 0 0.26 M

-x

x

x

Final

0.49-x

x

0.26+x

Initial 0.49 M 0 0.26 M

- Do the math
- Ka = 1.8 x 10-5

-x

x

x

Final

0.49-x

x

0.26+x

x (0.26)

x (0.26+x)

=

1.8 x 10-5 =

(0.49)

(0.49-x)

- Assume x is small

x = 3.4 x 10-5

- Assumption is valid
- pH = -log (3.4 x 10-5) = 4.47

Notice

- If we had added 0.010 mol of NaOH to 1 L of water, the pH would have been.
- 0.010 M OH-
- pOH = 2
- pH = 12
- But with a mixture of an acid and its conjugate base the pH doesn’t change much
- Called a buffer.

General equation

- Ka = [H+] [A-] [HA]
- so [H+] = Ka [HA] [A-]
- The [H+] depends on the ratio [HA]/[A-]
- taking the negative log of both sides
- pH = -log(Ka [HA]/[A-])
- pH = -log(Ka)-log([HA]/[A-])
- pH = pKa + log([A-]/[HA])

This is called the Henderson-Hasselbach equation

- pH = pKa + log([A-]/[HA])
- pH = pKa + log(base/acid)
- Works for an acid and its salt
- Like HNO2 and NaNO2
- Or a base and its salt
- Like NH3 and NH4Cl
- But remember to change Kb to Ka

Calculate the pH of the following

- 0.75 M lactic acid (HC3H5O3) and 0.25 M sodium lactate (Ka = 1.4 x 10-4)

- pH = 3.38

Calculate the pH of the following

- 0.25 M NH3 and 0.40 M NH4Cl (Kb = 1.8 x 10-5)
- Ka = 1 x 10-14 1.8 x 10-5
- Ka = 5.6 x 10-10
- remember its the ratio base over acid

- pH = 9.05

Prove they’re buffers

- What would the pH be if .020 mol of HCl is added to 1.0 L of both of the preceding solutions.
- What would the pH be if 0.050 mol of solid NaOH is added to 1.0 L of each of the proceeding.
- Remember adding acids increases the acid side,
- Adding base increases the base side.

Prove they’re buffers

- What would the pH be if .020 mol of HCl is added to 1.0 L of preceding solutions.
- 0.75 M lactic acid (HC3H5O3) and 0.25 M sodium lactate (Ka = 1.4 x 10-4)

HC3H5O3 H+ + C3H5O3-

Initially 0.75 mol 0 0.25 mol

After acid 0.77 mol 0.23 mol

Compared to 3.38 before acid was added

Prove they’re buffers

- What would the pH be if 0.050 mol of solid NaOH is added to 1.0 L of the solutions.
- 0.75 M lactic acid (HC3H5O3) and 0.25 M sodium lactate (Ka = 1.4 x 10-4)

HC3H5O3 H+ + C3H5O3-

Initially 0.75 mol 0 0.25 mol

After acid 0.70 mol 0.30 mol

Compared to 3.38 before acid was added

Prove they’re buffers

- What would the pH be if .020 mol of HCl is added to 1.0 L of preceding solutions.
- 0.25 M NH3 and 0.40 M NH4Cl Kb = 1.8 x 10-5 so Ka = 5.6 x 10-10

NH4+H+ + NH3

Initially 0.40 mol 0 0.25 mol

After acid 0.42 mol 0.23 mol

Compared to 9.05 before acid was added

Prove they’re buffers

- What would the pH be if 0.050 mol of solid NaOH is added to 1.0 L each solutions.
- 0.25 M NH3 and 0.40 M NH4Cl Kb = 1.8 x 10-5 so Ka = 5.6 x 10-10

NH4+H+ + NH3

Initially 0.40 mol 0 0.25 mol

After acid 0.35 mol 0.30 mol

Compared to 9.05 before acid was added

Buffer capacity

- The pH of a buffered solution is determined by the ratio [A-]/[HA].
- As long as this doesn’t change much the pH won’t change much.
- The more concentrated these two are the more H+ and OH- the solution will be able to absorb.
- Larger concentrations = bigger buffer capacity.

Buffer Capacity

- Calculate the change in pH that occurs when 0.040 mol of HCl(g) is added to 1.0 L of each of the following:
- 5.00 M HAc and 5.00 M NaAc
- 0.050 M HAc and 0.050 M NaAc
- Ka= 1.8x10-5
- pH = pKa

Buffer Capacity

- Calculate the change in pH that occurs when 0.040 mol of HCl(g) is added to 1.0 L of 5.00 M HAc and 5.00 M NaAc
- Ka= 1.8x10-5

HAc H+ + Ac-

Initially 5.00 mol 0 5.00 mol

After acid 5.04 mol 4.96 mol

Compared to 4.74 before acid was added

Buffer Capacity

- Calculate the change in pH that occurs when 0.040 mol of HCl(g) is added to 1.0 L of 0.050 M HAc and 0.050 M NaAc
- Ka= 1.8x10-5

HAc H+ + Ac-

Initially 0.050 mol 0 0.050 mol

After acid 0.090 mol 0 0.010 mol

Compared to 4.74 before acid was added

Buffer capacity

- The best buffers have a ratio [A-]/[HA] = 1
- This is most resistant to change
- True when [A-] = [HA]
- Makes pH = pKa (since log 1 = 0)

Titrations

- Millimole (mmol) = 1/1000 mol
- Molarity = mmol/mL = mol/L
- Makes calculations easier because we will rarely add liters of solution.
- Adding a solution of known concentration until the substance being tested is consumed.
- This is called the equivalence point.
- Where moles of acid = moles of base

Strong acid with Strong Base

- Do the stoichiometry.
- mL x M = mmol
- There is no equilibrium .
- They both dissociate completely.
- The reaction is H+ + OH- HOH
- Use [H+] or [OH-] to figure pH or pOH
- The titration of 20.0 mL of 0.10 M HNO3 with 0.10 M NaOH

Weak acid with Strong base

- There is an equilibrium.
- Do stoichiometry.
- Use moles
- Determine major species
- Then do equilibrium.

Calculate the pH after 0.0mL, 15.0mL, 25.0 mL, and 30.0mL of 0.10 M NaOH are added to 25.0mL of 0.10M of Nicotinic acid Ka= 1.4 x 10 -5

Summary

- Strong acid and base just stoichiometry.
- Weak acid with 0 ml of base - Ka
- Weak acid before equivalence point
- Stoichiometry first
- Then Henderson-Hasselbach
- Weak acid at equivalence point- Kb -Calculate concentration
- Weak acid after equivalence - leftover strong base. -Calculate concentration

Example

- A 25.0 mL sample of benzoic acid (0.120M) is titrated w/ NaOH (.210 M) Ka= 6.3 x 10 -5
- Calculate # moles of Benzoic acid
- Calculate volume of NaOH needed to reach equiv. pt
- Calc. the pH before any base is added
- Calc. pH after 10ml base is added
- Find the pH at equivalence pt
- Calculate the pH after 15.3mL of OH- is added

Summary

- Weak base before equivalence point.
- Stoichiometry first
- Then Henderson-Hasselbach
- Weak base at equivalence point Ka. -Calculate concentration
- Weak base after equivalence – left over strong acid. -Calculate concentration

Indicators

- Weak acids that change color when they become bases.
- weak acid written HIn
- Weak base
- HIn H+ + In-clear red
- Equilibrium is controlled by pH
- End point - when the indicator changes color.
- Try to match the equivalence point

Indicators

- Since it is an equilibrium the color change is gradual.
- It is noticeable when the ratio of [In-]/[HI] is 1/10 or [HI]/[In-] is 10/1
- Since the Indicator is a weak acid, it has a Ka.
- pH the indicator changes is
- pH=pKa +log([In-]/[HI]) = pKa +log(1/10)
- pH=pKa - 1

Indicators

- pH=pKa + log([HI]/[In-]) = pKa + log(10)
- pH=pKa+1
- Choose the indicator with a pKa 1 more than the pH at equivalence point if you are titrating with base.
- Choose the indicator with a pKa 1 less than the pH at equivalence point if you are titrating with acid.

Sample Problem

- Two drops of indicator HIn (Ka= 1.0 x 10 -9), hwere HIn is yellow and In- is blue are placed in 100.0 mL of 0.10 M HCl.
- What color is the solution initially?
- The solution is titrated with 0.10 M NaOH. At what pH will the color change (greenish yellow) occur?
- What color will the solution be after 200.0mL of NaOH has been added?

Will it all dissolve, and if not, how much?

All dissolving is an equilibrium.

- If there is not much solid it will all dissolve.
- As more solid is added the solution will become saturated.
- Solid dissolved
- The solid will precipitate as fast as it dissolves .
- Equilibrium

General equation

- M+ stands for the cation (usually metal).
- Nm-stands for the anion (a nonmetal).
- MaNmb(s) aM+(aq) + bNm- (aq)
- Remember the concentration of a solid doesn’t change. So, what’s the K expression?
- Ksp = [M+]a[Nm-]b
- Called the solubility product for each compound.

Watch out

- Solubility is not the same as solubility product.
- Solubility product is an equilibrium constant.
- it doesn’t change except with temperature.
- Solubility is an equilibrium position-usually expressed as a Molarity for how much can dissolve.

Calculating Solubility

Ex: Calc. Solubility of CaC2O4 if the value of Ksp= 4.8 x 10 -5 mol/L

CaC2O4 (s) ↔ Ca+2(aq) + C2O4 -2 (aq)

Ksp = [Ca+2] [C2O4-2]

Ksp= [s] [s] = [s]2 = 4.8x10-5 = s2

s= 6.9 x 10 -3 M

Calculating Ksp

- The solubility of copper(I) bromide is

2.0 x 10 -4 mol/L. Calc. Ksp value.

CuBr(s) ↔ Cu+1(aq) + Br-1 (aq)

I .0002M 0M 0M

C - .0002M +.0002M +.0002M

E 0 .0002M .0002M

Ksp = [.0002] [.0002] = 4.0 x 10 -8

(units usually omitted)

Calculating Ksp

- The solubility of iron(II) oxalate FeC2O4 is 65.9 mg/L
- The solubility of Li2CO3 is 5.48 g/L

Common Ion Effect

- If we try to dissolve the solid in a solution with either the cation or anion already present less will dissolve.
- Calculate the solubility of SrSO4, with a Ksp of 3.2 x 10-7 in M in a solution of 0.010 M Na2SO4.
- Calculate the solubility of CaF2

Ksp= 4.0 x 10 -11 in a 0.025 M NaF solution.

AgCl and NaCl in solution

- Cl- is the common ion
- When [Ag+] [Cl-] < Ksp, no precipitate will be formed.
- When [Ag+] [Cl-] > Ksp, a precipitate will be formed.

pH and solubility

- OH- can be a common ion.
- More soluble in acid.
- For other anions if they come from a weak acid they are more soluble in a acidic solution than in water.
- CaC2O4 Ca+2 + C2O4-2
- H+ + C2O4-2 HC2O4-
- Reduces [C2O4-2] in acidic solution.

Sample problem

- What is the pH in a saturated solution of Ca(OH)2?Ksp = 5.5 x 10-6 for Ca(OH)2.

Q and Precipitation

- not necessarily at Equil.
- Q= Ion product
- Q =[M+]a[Nm-]b
- If Q>Ksp a precipitate forms. (supersaturated)
- If Q<Ksp No precipitate. (unsaturated)
- If Q = Ksp equilibrium. (saturated)

Example1

Chemical analysis gave [Pb2+] = 0.012 M, and [Br-] = 0.024 M in a solution. From a table, you find Ksp for PbBr2 has a value of 4x 10-5. Is the solution saturated, oversaturated or unsaturated?

Example 2

- A solution of 750.0 mL of 4.00 x 10-3M Ce(NO3)3 is added to 300.0 mL of 2.00 x 10-2M KIO3. Will Ce(IO3)3 (Ksp= 1.9 x 10-10M) precipitate and if so, what is the concentration of the ions?

Selective Precipitations

- Used to separate mixtures of metal ions in solutions.
- Add anions that will only precipitate certain metals at a time.
- Used to purify mixtures.
- Often use H2S because in acidic solution Hg+2, Cd+2, Bi+3, Cu+2, Sn+4 will precipitate.

Selective Precipitation

- Then add OH-solution [S-2] will increase so more soluble sulfides will precipitate.
- Co+2, Zn+2, Mn+2, Ni+2, Fe+2, Cr(OH)3, Al(OH)3

Selective precipitation

- Follow the steps
- First with insoluble chlorides (Ag, Pb, Ba)
- Then sulfides in Acid.
- Then sulfides in base.
- Then insoluble carbonate (Ca, Ba, Mg)
- Alkali metals and NH4+ remain in solution.

Complex ion Equilibria

- A charged ion surrounded by ligands.
- Ligands are Lewis bases using their lone pair to stabilize the charged metal ions.
- Common ligands are NH3, H2O, Cl-,CN-
- Coordination number is the number of attached ligands.
- Cu(NH3)42+ has a coordination # of 4

The addition of each ligand has its own equilibrium

- Usually the ligand is in large excess.
- And the individual K’s will be large so we can treat them as if they go to completion.
- The complex ion will be the biggest ion in solution.

Calculate the concentrations of Ag+, Ag(S2O3)-2, and Ag(S2O3)2-3 in a solution made by mixing 150.0 mL of 0.010 M AgNO3 with 200.0 mL of 5.00 M Na2S2O3

- Ag+ + S2O3-2 Ag(S2O3)- K1=7.4 x 108
- Ag(S2O3)- + 2S2O3-2 Ag(S2O3)2-3 K2=3.9 x 104

(Hint: set up ice problem, determine L.R.)

This problem is found on pg. 768-769 in your book. Check your work!

Complex Ions and Solubility

The dissolving of solid AgCl in excess NH3 is represented as…

AgCl(s) + 2NH3(aq) ↔ Ag(NH3)2+ (aq) + Cl-(aq)

However, this is a result of several steps

AgCl(s) ↔ Ag+ + Cl- Ksp= 1.6 x 10-10

Ag+ + NH3 ↔ Ag(NH3)+ K1 = 2.1 x 103

Ag(NH3)+ + NH3 ↔ Ag(NH3)2+ K2= 8.2 x 103

AgCl(s) + 2NH3(aq) ↔ Ag(NH3)2+ (aq) + Cl-(aq)

So the Equilibrium Expression is written as…. K= [Ag(NH3)2+] [Cl-]

[NH3]2

= Ksp x K1 x K2

= (1.6 x 10-10) ( 2.1 x 103) (8.2 x 103)

= 2.8 x 10-3

Summary

3 Factors that affect solubility:

- Common Ions

- pH

- Complexing Agents/Ions

Mixtures of Ions can be separated by selective precipitation (you know this as Quantitative Analysis)

- Steps listed on pg.765 or in your lab

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